Answers25-26 MISD Geometry A - CRUnit Test

Incenter and Circumcenter Answers

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1
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Which is the only center point that lies on the edge of a triangle?

A
the incenter of a right triangle
B
the incenter of an obtuse triangle
C
the circumcenter of a right triangle
D
the circumcenter of an obtuse triangle
2
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The figure shows a circle circumscribed around a triangle.

Question illustration
A
perpendicular segments to the vertices of the triangle
B
perpendicular bisectors of the sides of the triangle
C
angle bisectors of each angle of the triangle
D
the incenter of the triangle
3

In the diagram, Z is the circumcenter of triangle TUV.

Question illustration
A
2 units
B
6 units
C
8 units
D
10 units
4

Point G is the incenter of the triangle.

Question illustration
A
4
B
8
C
24
D
32
5

Point X is the circumcenter of ΔABC.

Question illustration
A
1.5 cm
B
2 cm
C
2.5 cm
D
3 cm
6

Point A is inside triangle E D F. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A L, A M, and A N. The length of A E is 10 and the length of A D is 2 n + 4.

Question illustration
A
2
B
3
C
4
D
5
7

Point A is the incenter of ΔDEF.

Question illustration
A
7
B
11
C
14
D
15
8

Which must be true? Select three options

A
Point A is the center of the circle that passes through points D, E, and F.
B
Point A is the center of the circle that passes through points X, Y, and Z.
C
Line segment Z A is-congruent-to line segment Y A
Option C
D
Line segment E A is-congruent-to line segment F A
Option D
E
Line segment A X is-congruent-to line segment A Y
Option E
9

Point P is the incenter of ΔRST.

Question illustration
A
Line segment C P is-congruent-to line segment R P
Option A
B
Line segment B P is-congruent-to line segment P C
Option B
C
PSC PTC
Option C
D
BPS APT
Option D
10

Point A is the point of concurrency of the angle bisectors of ΔDEF.

Question illustration
A
ZA = 3cm
B
ZA = 4cm
C
ZA = 5cm
D
ZA = 6cm
11

Three friends want to meet at a place that is the same distance from each of their houses. They draw a map and measure the approximate distances and angles, as shown.

Question illustration
A
Find the midpoint of the segments which connect their houses.
B
Bisect each of the angles with vertices at their houses.
C
Draw perpendicular lines through any point on the segments which connect their houses.
D
Draw perpendicular line segments from each vertex to the opposite side.
12

Point Z is the incenter of triangle RST.

Question illustration
A
x = 2
B
x = 3
C
x = 5
D
x = 8
13

The figure shows a circle inscribed in a triangle.

Question illustration
A
A circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.
B
A circle was constructed using a vertex as the center of the circle and the intersection of the angle bisectors as a point on the circumference of the circle.
C
Segments perpendicular to the sides of the triangle through the intersection of the angle bisectors were constructed.
D
Segments bisecting each side of the triangle were constructed through the intersection of the angle bisectors.
14

Point Y is the circumcenter of triangle DEF.

Question illustration
A
Point Y is the center of the circle that passes through points D, F, and N.
B
Point Y is the center of the circle that passes through points M, N, and E.
C
Point Y is the center of the circle that passes through points L, M, and N.
D
Point Y is the center of the circle that passes through points D, E, and F.
15

Point O is the incenter of triangle ABC.

Question illustration
A
30°
B
60°
C
75°
D
90°
16

Point H is the circumcenter of ΔJKL.

Question illustration
A
Line segment F H is-congruent-to line segment D H
Option A
B
Line segment J F is-congruent-to line segment L H
Option B
C
Line segment J H is-congruent-to line segment L H
Option C
D
Line segment K F is-congruent-to line segment L D
Option D
17

Point Y is the circumcenter of ΔDEF.

Question illustration
A
5
B
11
C
17
D
22
18

Point A is the incenter of ΔDEF.

Question illustration
A
2 units
B
9 units
C
11 units
D
14 units

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